MAH-MHT CET (PCM/PCB) entrance exam Question Bank Solutions for Mathematics

For the LPP, maximize z = x + 4y subject to the constraints x + 2y ≤ 2, x + 2y ≥ 8, x, y ≥ 0 ______.

The maximum value of z = 3x + 10y subjected to the conditions 5x + 2y ≤ 10, 3x + 5y ≤ 15, x, y ≥ 0 is ______.

If the origin and the points P(2, -7, 5), Q(2, 3, - 5) and R(x, y, z) are co-planar, then ______ 

`int "e"^x [2"cosec"  2x + log(tanx)] "d"x` = ______.

The constraints of an LPP are 7 ≤ x ≤ 12, 8 ≤ y ≤ 13. Determine the vertices of the feasible region formed by them.

The point which provides the solution to the linear programming problem: Max P = 2x + 3y subject to constraints: x ≥ 0, y ≥ 0, 2x + 2y ≤ 9, 2x + y ≤ 7, x + 2y ≤ 8, is ______ 

`int("I" - cosx)"cosec"^2x"d"x` = ______.

The negation of the statement "If you don't work bard you will not become successful." is ______ 

If `int (sin2x)/(sin^4x + cos^4x) "d"x = tan^-1["f"(x)] + "c"`, then `"f"(pi/3)` = ______.

The Standard deviation of the following frequency distribution

is ______.

If f(x) =x⁴, g(x) = 6x – 2, then g[f(x)] = ______.

If 4x + 5y ≤ 20, x + y ≥ 3, x ≥ 0, y ≥ 0, maximum 2x + 3y is ______.

`int (cot(logx))/x "d"x` = ______.

`int "e"^sintheta [log(sin theta) + "cosec"^2theta]costheta "d"theta` = ______.

`int (sec^8x)/("cosec" x)  "d"x` = ______.

The maximum of z = 5x + 2y, subject to the constraints x + y ≤ 7, x + 2y ≤ 10, x, y ≥ 0 is ______.

A random variable X has the following probability distribution:

Then, the expected value of X is ______.

Negation of (∼p → q) is ______.

`int cosx/sqrt(1 + sinx) "d"x` = ______.

Inverse of the function y = 5 – 10x is ______.